Question

Dairy Queen has been analyzing their sales and profit records. They came up
with the following equations:
A. The function below shows Profit, P, as a function of the cost of a blizzard x.
P(x) - 65(x - 4) + 1000
=
1. At what prices would Dairy Queen earn zero profit?
2. How should Dairy Queen price their blizzards to maximize profits?
3. What is their estimated maximum profit?
4. Sketch a graph and make sure to label the x and y axis.

Answer 1

The function P(x) = -65(x - 4)² + 1000 of Dairy queen is an illustration of quadratic functions

Dairy queen should price their blizzards at $4, and the estimated maximum profit is $1000

The price that gives zero profit

The function is given as:

P(x) = -65(x - 4)² + 1000

At zero profit, P(x) = 0

So, we have:

-65(x - 4)² + 1000 = 0

From the graph of the function (see attachment), we have:

x = 0.078 and x = 7.922

Hence, the prices that give zero profit are 0.078 and 7.922

How to maximize profits?

To maximize profit, Dairy Queen should their blizzards at a price that yields maximum profit

The estimated maximum profit

We have:

P(x) = -65(x - 4)² + 1000

A quadratic function is represented as:

P(x) = a(x - h)² + k

Where:

Vertex = (h,k)

So, we have:

h = 4 and k = 1000

Hence, Dairy queen should price their blizzards at $4, and the estimated maximum profit is $1000

Read more about quadratic functions at:

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